This paper develops a physically consistent signal model with hardware constraints for a simultaneous transmitting and reflecting beyond-diagonal RIS (STAR BD-RIS) endowed with per-element amplification and lossless power splitting. We explicitly decouple (i) amplification via a diagonal gain matrix, (ii) element-wise reflection/transmission splitting, and (iii) passive beyond-diagonal coupling on each branch, while enforcing practical feasibility through per-element emission caps and an aggregate RIS power budget under the operating covariance. Building on this model, we cast downlink sum-rate maximization as an equivalent weighted minimum mean-square error (WMMSE) problem and propose an alternating optimization framework with provable monotonic descent. The method admits closed-form updates for MMSE combiners and weights, waterfilling-like beamformer updates via a single dual variable, a per-element amplification update that satisfies emission constraints, and a STAR power-splitting update based on cyclic coordinate descent with a global acceptance test. For the beyond-diagonal coupling matrices, we derive Riemannian gradient steps on the complex Stiefel manifold with QR/polar retraction method, preserving passivity at every iterate. Furthermore, the proposed approach decouples the optimization of the reflective and transmissive responses of the BD-RIS, enabling efficient distributed implementation. Numerical results demonstrate substantial sum-rate gains compared to the conventional passive BD-RIS.

翻译：本文针对配备单元级放大与无损功率分配功能的超对角同时收发智能反射面（STAR BD-RIS），建立了一个符合物理实际且包含硬件约束的信号模型。我们明确解耦了三个关键部分：（1）通过对角增益矩阵实现的放大功能；（2）单元级的反射/透射功率分配；（3）各支路上的无源超对角耦合机制，同时通过单元发射功率上限及工作协方差下的总RIS功率预算来确保实际可行性。基于该模型，我们将下行链路和速率最大化问题转化为等效的加权最小均方误差（WMMSE）问题，并提出一种具有可证明单调下降特性的交替优化框架。该方法支持以下闭式更新：MMSE合并器与权重、通过单一对偶变量实现类注水算法的波束成形器更新、满足发射约束的单元级放大系数更新，以及基于带全局接受判据的循环坐标下降法的STAR功率分配更新。对于超对角耦合矩阵，我们推导了复Stiefel流形上的黎曼梯度步进算法，并采用QR/极坐标回缩方法，确保每次迭代均保持无源性。此外，所提方法解耦了BD-RIS反射与透射响应的优化，支持高效的分布式实现。数值结果表明，与传统无源BD-RIS相比，本方案能带来显著的和速率增益。